Properties

Label 20.12.a
Level 20
Weight 12
Character orbit a
Rep. character \(\chi_{20}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 2
Sturm bound 36
Trace bound 1

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Defining parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 20.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(36\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(20))\).

Total New Old
Modular forms 36 3 33
Cusp forms 30 3 27
Eisenstein series 6 0 6

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(5\)FrickeDim.
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(2\)
Minus space\(-\)\(1\)

Trace form

\(3q \) \(\mathstrut +\mathstrut 526q^{3} \) \(\mathstrut +\mathstrut 3125q^{5} \) \(\mathstrut -\mathstrut 28734q^{7} \) \(\mathstrut -\mathstrut 39773q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut 526q^{3} \) \(\mathstrut +\mathstrut 3125q^{5} \) \(\mathstrut -\mathstrut 28734q^{7} \) \(\mathstrut -\mathstrut 39773q^{9} \) \(\mathstrut +\mathstrut 293040q^{11} \) \(\mathstrut +\mathstrut 1437654q^{13} \) \(\mathstrut -\mathstrut 268750q^{15} \) \(\mathstrut +\mathstrut 3959022q^{17} \) \(\mathstrut +\mathstrut 3160332q^{19} \) \(\mathstrut +\mathstrut 32048108q^{21} \) \(\mathstrut +\mathstrut 22871382q^{23} \) \(\mathstrut +\mathstrut 29296875q^{25} \) \(\mathstrut -\mathstrut 31679468q^{27} \) \(\mathstrut +\mathstrut 39728922q^{29} \) \(\mathstrut +\mathstrut 153568188q^{31} \) \(\mathstrut -\mathstrut 114594960q^{33} \) \(\mathstrut +\mathstrut 110668750q^{35} \) \(\mathstrut -\mathstrut 838367994q^{37} \) \(\mathstrut -\mathstrut 977016388q^{39} \) \(\mathstrut +\mathstrut 593660058q^{41} \) \(\mathstrut -\mathstrut 16928250q^{43} \) \(\mathstrut +\mathstrut 397653125q^{45} \) \(\mathstrut -\mathstrut 1145164758q^{47} \) \(\mathstrut -\mathstrut 291676881q^{49} \) \(\mathstrut -\mathstrut 2443209204q^{51} \) \(\mathstrut +\mathstrut 3824525838q^{53} \) \(\mathstrut +\mathstrut 948750000q^{55} \) \(\mathstrut +\mathstrut 2831715224q^{57} \) \(\mathstrut +\mathstrut 6558500604q^{59} \) \(\mathstrut -\mathstrut 4737293274q^{61} \) \(\mathstrut +\mathstrut 11880551714q^{63} \) \(\mathstrut +\mathstrut 3068706250q^{65} \) \(\mathstrut +\mathstrut 2526990306q^{67} \) \(\mathstrut -\mathstrut 1519195644q^{69} \) \(\mathstrut -\mathstrut 55526135916q^{71} \) \(\mathstrut +\mathstrut 51700617654q^{73} \) \(\mathstrut +\mathstrut 5136718750q^{75} \) \(\mathstrut -\mathstrut 15515642160q^{77} \) \(\mathstrut -\mathstrut 32040411384q^{79} \) \(\mathstrut -\mathstrut 61073448953q^{81} \) \(\mathstrut +\mathstrut 56064195942q^{83} \) \(\mathstrut +\mathstrut 44230181250q^{85} \) \(\mathstrut -\mathstrut 121965495516q^{87} \) \(\mathstrut -\mathstrut 9837283362q^{89} \) \(\mathstrut -\mathstrut 136246479228q^{91} \) \(\mathstrut +\mathstrut 256570464296q^{93} \) \(\mathstrut +\mathstrut 111620012500q^{95} \) \(\mathstrut -\mathstrut 89661136554q^{97} \) \(\mathstrut -\mathstrut 25109887440q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(20))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5
20.12.a.a \(1\) \(15.367\) \(\Q\) None \(0\) \(306\) \(-3125\) \(-32074\) \(-\) \(+\) \(q+306q^{3}-5^{5}q^{5}-32074q^{7}-83511q^{9}+\cdots\)
20.12.a.b \(2\) \(15.367\) \(\Q(\sqrt{46729}) \) None \(0\) \(220\) \(6250\) \(3340\) \(-\) \(-\) \(q+(110-\beta )q^{3}+5^{5}q^{5}+(1670-111\beta )q^{7}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(20))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(20)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 2}\)